We investigate the radiation properties of a short horizontal dipole embedded in a uniaxial wire medium. It is shown that the uniaxial wire medium enables a super-collimation of the dipole radiation such that the radiation pattern has a singularity and the radiated fields are non-diffractive in the broadside direction. We derive a closed analytical formula for the power radiated by the dipole in the wire medium. Our theory demonstrates that as a consequence of the ultrahigh density of photonic states of the nanowire array, the power radiated by the dipole is strongly enhanced as compared to the power that would be emitted in the dielectric host with no nanowires.